Answer:
x-intercepts = 1,2, and 4, y-intercept = -8
Step-by-step explanation:
x^3 - 7x^2 - 14x - 8 in factored form is equal to (x-1)(x-2)(x-4).
Solving for x-intercepts:
- We are actually able to solve for all x-intercepts without the given factor. But since we are given one of the factors, our job becomes much easier.
- Using synthetic division, or long division, we factor out the x-intercept 4. Which leaves us with the polynomial x^2 - 3x + 2.
- From here we can separate the polynomial into two binomials.
- x^2 - 3x + 2 = (x-1)(x-2). Giving us all 3 x-intercepts.
- Using Descartes' rules we can identify before even starting the problem how many real x-intercepts there are (Not needed for this problem).
Solving for y-intercept:
- The y-intercept is always the coefficient that does not have any assigned x-variables.
- The coefficient is -8, thus the y-intercept.
- If unsure of the y-intercept, you can always plug in x = 0. Solving for the y-intercept will give you the value of f(0).
- If there is no coefficient, the y-intercept is equal to zero.
The area of the given square pyramid is:
total area = 1,100 inches squared.
<h3 /><h3>
How to get the area of the pyramid?</h3>
On the second image, we can see that the pyramid is conformed of a square base and 3 triangles.
To get the surface area of the pyramid, we can just get the area of each of these simpler parts.
The base is a square of 22 in by 22 in, then the area of the base is:
B = (22in)*(22 in) = 484 in^2
For each triangle, the area will be:
A = (base side)*(height)/2
A = (22in)*(14in)/2 = 154 in^2
And we have 4 of these triangles, then the total area of the pyramid will be:
total area = B + 4*A = 484in^2 + 4*(154 in^2) = 1,100 in^2
If you want to learn more about square pyramids:
brainly.com/question/22744289
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